91Ó°ÊÓ

The sum of the first 20 terms of an arithmetic progression whose first term is 5 and common differen is 4 , is (1) 820 (2) 830 (3) 850 (4) 860

Three alternate terms of an arithmetic progression are \(x+y, x-y\) and \(2 x+3 y\), then \(x=\) (1) - y (2) \(-2 \mathrm{y}\) (3) \(-4 y\) (4) -6y

If the 3rd, 7 th and 11 th terms of a geometric progression are \(\mathrm{p}, \mathrm{q}\) and \(\mathrm{r}\) respectively, then the relation among \(\mathrm{p}, \mathrm{q}\) and \(\mathrm{r}\) is (1) \(\mathrm{p}^{2}=\mathrm{qr}\) (2) \(\mathrm{r}^{2}=\mathrm{qp}\) (3) \(\mathrm{q}^{2}=\mathrm{p}^{2} \mathrm{r}^{2}\) (4) \(\mathrm{q}^{2}=\mathrm{pr}\)

Five distinct positive integers are in arithmetic progression with a positive common difference. If their sum is 10020 , then find the smallest possible value of the last term. (1) 2002 (2) 2004 (3) 2006 (4) 2008

If \(a, b\) and \(c\) are positive numbers in arithmetic progression. and \(a^{2}, b^{2}\) and \(c^{2}\) are in geometric progression then \(\mathrm{a}^{3}, \mathrm{~b}^{3}\) and \(\mathrm{c}^{3}\) are in (a) Arithmetic Progression (b) Geometric Progression (c) Harmonic Progression (1) (a) and (b) only (2) only (c) (3) (a), (b) and (c) (4) only (b)

The numbers \(\mathrm{h}_{1}, \mathrm{~h}_{2}, \mathrm{~h}_{3}, \mathrm{~h}_{4}, \ldots \ldots, \mathrm{h}_{10}\) are in harmonic progression and \(\mathrm{a}_{1}, \mathrm{a}_{2}, \ldots, \mathrm{a}_{10}\) are in arithmetic progression. If \(a_{1}=h_{1}=3\) and \(a_{7}=h_{7}=39\), then the value of \(a_{4} \times h_{4}\) is (1) \(\frac{13}{49}\) (2) \(\frac{182}{3}\) (3) \(\frac{7}{13}\) (4) 117

Find the sum of all natural numbers and lying between 100 and 200 which leave a remainder of 2 when divided by 5 in each case. (1) 2990 (2) 2847 (3) 2936 (4) None of these

An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11 terms is 33 , then find the fourth term. (1) 2 (2) 3 (3) 5 (4) 6

If the sum of 16 terms of an AP is 1624 and the first term is 500 times the common difference, then find the common difference. (1) 5 (2) \(1 / 2\) (3) \(1 / 5\) (4) 2

Find the sum of the series \(1+(1+2)+(1+2+3)+(1+2+3+4)+\ldots+(1+2+3+\ldots .+20)\). (1) 1470 (2) 1540 (3) 1610 (4) 1370